Scalable Quantum Computational Science: A Perspective from Block-Encodings and Polynomial Transformations
arXiv:2511.16738 · doi:10.1063/5.0312254
Abstract
Significant developments made in quantum hardware and error correction recently have been driving quantum computing towards practical utility. However, gaps remain between abstract quantum algorithmic development and practical applications in computational sciences. In this Perspective article, we propose several properties that scalable quantum computational science methods should possess. We further discuss how block-encodings and polynomial transformations can potentially serve as a unified framework with the desired properties. Recent advancements on these topics are presented including construction and assembly of block-encodings, and various generalizations of quantum signal processing (QSP) algorithms to perform polynomial transformations. The scalability of QSP methods on parallel and distributed quantum architectures is also highlighted. Promising applications in simulation and observable estimation in chemistry, physics, and optimization problems are presented. We hope this Perspective serves as a gentle introduction of state-of-the-art quantum algorithms to the computational science community, and inspires future development on scalable quantum computational science methodologies that bridge theory and practice.
References in corpus (74)
- A variational eigenvalue solver on a quantum processor
- Variational Quantum Algorithms
- Barren plateaus in quantum neural network training landscapes
- Noisy intermediate-scale quantum (NISQ) algorithms
- Quantum Chemistry in the Age of Quantum Computing
- NMR Techniques for Quantum Control and Computation
- Logical quantum processor based on reconfigurable atom arrays
- Hamiltonian Simulation by Qubitization
- Optimal Hamiltonian Simulation by Quantum Signal Processing
- Simulating Hamiltonian dynamics with a truncated Taylor series
- Quantum error correction below the surface code threshold
- Quantum Simulators: Architectures and Opportunities
- Toward the first quantum simulation with quantum speedup
- Variational ansatz-based quantum simulation of imaginary time evolution
- Real-time quantum error correction beyond break-even
- New class of quantum error-correcting codes for a bosonic mode
- tket : A Retargetable Compiler for NISQ Devices
- Polynomial-time quantum algorithm for the simulation of chemical dynamics
- Quantum control of molecular rotation
- Accelerated Variational Quantum Eigensolver
- Efficient Distributed Quantum Computing
- Sampling from the thermal quantum Gibbs state and evaluating partition functions with a quantum computer
- Optimal Quantum Measurements of Expectation Values of Observables
- Efficient Bayesian Phase Estimation
- Beating the break-even point with a discrete-variable-encoded logical qubit
- Experimental Bayesian Quantum Phase Estimation on a Silicon Photonic Chip
- Distributed Quantum Computing across an Optical Network Link
- A divide-and-conquer algorithm for quantum state preparation
- Near-optimal ground state preparation
- Efficient phase-factor evaluation in quantum signal processing
- The methodology of resonant equiangular composite quantum gates
- Measurements as a roadblock to near-term practical quantum advantage in chemistry: resource analysis
- Quantum Krylov subspace algorithms for ground and excited state energy estimation
- Encoding a magic state with beyond break-even fidelity
- Quantum Inference on Bayesian Networks
- Hardware-efficient quantum error correction via concatenated bosonic qubits
- Quantum Simulation of Chemistry with Sublinear Scaling in Basis Size
- Quantum-centric Supercomputing for Materials Science: A Perspective on Challenges and Future Directions
- Product Decomposition of Periodic Functions in Quantum Signal Processing
- Minimizing estimation runtime on noisy quantum computers
- Simulating Open Quantum Systems Using Hamiltonian Simulations
- Efficient Fully-Coherent Quantum Signal Processing Algorithms for Real-Time Dynamics Simulation
- Quantum Error Correction of Qudits Beyond Break-even
- Optimal arbitrarily accurate composite pulse sequences
- Approximate Quantum Circuit Synthesis using Block-Encodings
- Quantum algorithm for time-dependent Hamiltonian simulation by permutation expansion
- On the complexity of implementing Trotter steps
- Multivariable quantum signal processing (M-QSP): prophecies of the two-headed oracle
- Amplitude Estimation from Quantum Signal Processing
- On the Sample Complexity of Quantum Boltzmann Machine Learning
- Hybrid Oscillator-Qubit Quantum Processors: Instruction Set Architectures, Abstract Machine Models, and Applications
- Stable factorization for phase factors of quantum signal processing
- Fragmented imaginary-time evolution for early-stage quantum signal processors
- Chiral symmetry in non-Hermitian systems: product rule and Clifford algebra
- Diagonalization of large many-body Hamiltonians on a quantum processor
- Minimal Effective Gibbs Ansatz (MEGA): A simple protocol for extracting an accurate thermal representation for quantum simulation
- Bootstrap Embedding on a Quantum Computer
- Doubling Efficiency of Hamiltonian Simulation via Generalized Quantum Signal Processing
- Quantum Simulations of Chemistry in First Quantization with any Basis Set
- Dissipative Preparation of Many-Body Quantum States: Towards Practical Quantum Advantage
- Infinite quantum signal processing
- Efficient explicit gate construction of block-encoding for Hamiltonians needed for simulating partial differential equations
- Parallel Quantum Algorithm for Hamiltonian Simulation
- Toward Mixed Analog-Digital Quantum Signal Processing: Quantum AD/DA Conversion and the Fourier Transform
- Block encoding bosons by signal processing
- Halving the Cost of Quantum Algorithms with Randomization
- Single-shot Quantum Signal Processing Interferometry
- Complementary polynomials in quantum signal processing
- Exact block encoding of imaginary time evolution with universal quantum neural networks
- Ladder Operator Block-Encoding
- Solving Free Fermion Problems on a Quantum Computer
- Infinite quantum signal processing for arbitrary Szegő functions
- Parallel Quantum Signal Processing Via Polynomial Factorization
- Classical optimization with imaginary time block encoding on quantum computers: The MaxCut problem